How to align one vertex to X, Y or Z of another vertex
To do that quicker, 

first method

set the pivot point to active element and start your cut from the existing point (as this will keep this point active).

Then scale to 0 using the wanted axis :



second method

Use 'offset edge slide' Shift+Ctrl+R.

During the movement place the mouse along the shortest edge and hit E.

After that you'll need to remove doubles or merge the vertices.